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**Noise in Short Channel MOSFETs**

John A. McNeill Worcester Polytechnic Institute (WPI), Worcester, MA

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**Overview Creativity in Analog / Mixed Signal IC Design**

DSM CMOS Effects on Analog Design Fundamental Noise Sources Applications Conclusion

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**Overview Creativity in Analog / Mixed Signal IC Design**

Role of Creativity DSM CMOS Effects on Analog Design Fundamental Noise Sources Applications Conclusion

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**Career Classification**

CREATIVE USEFUL ARTIST POET TEACHER NURSE PROFESSOR ENGINEER ADVERTISING DOCTOR INVESTMENT BANKER LAWYER GOOD PAY

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**Why be creative? Need Easy problems solved already**

Tough problems need creative solution Dealing with environment of change Coping vs. thriving Human nature Fun!

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Creativity Resources

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Creativity Framework Explorer Artist Judge Warrior

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**Example: Time (Stages of project)**

Explorer Artist Judge Warrior Background Research Brainstorm Options Choose Solution Implement Design

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**Creativity Framework Explorer Artist Judge Warrior**

Seek out new information Survey the landscape Get off the beaten path Poke around in unrelated areas Gather lots of ideas Shift your mindset Don't overlook the obvious Look for unusual patterns

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**Creativity Framework Explorer Artist Judge Warrior**

Create something original Multiply options Use your imagination Ask "what if" questions Play with ideas Look for hidden analogies Break the rules Look at things backward Change contexts Play the fool

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**Creativity Framework Explorer Artist Judge Warrior Evaluate options**

Ask what's wrong Weigh the risk Embrace failure Question assumptions Look for hidden bias Balance reason and hunches Make a decision!

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**Creativity Framework Explorer Artist Judge Warrior**

Put decision into practice Commit to a realistic plan Get help Find your real motivation See difficulty as challenge Avoid excuses Persist through criticism Sell benefits not features Make it happen Learn from every outcome

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**Example: Modes of Thinking**

Explorer Artist Judge Warrior Divergent Soft Qualitative Convergent Hard Quantitative

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**Why a Creativity Model? Education Standardized-test-numbed students**

Paralysis in face of open-ended problem Designer Awareness of strengths, weaknesses Recognize preferences Not Right or Wrong! One way of looking at process Orchard analogy

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**Creativity Framework Explorer Artist Judge Warrior**

Survey the landscape Break the rules Question assumptions Learn from every outcome

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**Overview Creativity in Analog / Mixed Signal IC Design**

DSM CMOS Effects on Analog Design Short Channel Effects Noise Behavior Fundamental Noise Sources Applications Conclusion Survey the landscape

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**Good Old Days W/L ID Large strong inversion “square law” region**

WEAK INVERSION VELOCITY SATURATION Large strong inversion “square law” region “Easy hand analysis Op 't Eynde and Sansen, "Design and Optimization of CMOS Wideband Amplifiers," CICC 1989

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**TSMC L=0.25µm process W [µm] ID [µA] Square law**

104 W [µm] WEAK INVERSION 103 102 101 VELOCITY SATURATION ID [µA] 100 10-6 10-5 10-4 10-3 10-2 Square law Graphical / numerical analysis

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MOSFET Noise Y. Tsividis, "Operation and Modeling of the MOS Transistor" New York: Oxford University Press, 2008.

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**MOSFET Noise p.s.d. Saturation, strong inversion operation**

[A2/Hz] 1/f REGION WHITE NOISE REGION Saturation, strong inversion operation Where does factor g=2/3 come from? Y. Tsividis, "Operation and Modeling of the MOS Transistor" New York: Oxford University Press, 2008.

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**Submicron CMOS: Noise behavior**

Gamma factor g > 2/3 ?!? Disagreement with long channel model? Question assumptions Navid, Lee, and Dutton," A Circuit-Based Noise Parameter Extraction Technique for MOSFETs," ISCAS 2007, pp

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**Overview Creativity in Analog / Mixed Signal IC Design**

DSM CMOS Effects on Analog Design Fundamental Noise Sources Shot Noise Thermal Noise Applications Conclusion

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**Shot Noise Current noise density for DC current IDC**

Where does this come from? Key assumption: Electron arrivals independent events

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Shot Noise What is current measured by ammeter?

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Shot Noise What is current measured by ammeter?

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**Ramo-Shockley Theorem**

Current measured by ammeter: Randomly arriving pulses with area qe

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**Poisson Process Average arrival rate [sec-1] Average DC current:**

AUTOCORRELATION Average arrival rate [sec-1] Average DC current: Autocorrelation: time domain description of random process

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**Shot Noise Power Spectral Density**

Wiener-Khinchine theorem Autocorrelation frequency domain p.s.d Frequency domain For frequencies < 1/T

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**Shot Noise Power Spectral Density**

Key Points: Discrete nature of charge is essential Carrier transits are independent events Carriers do not interact with each other or with any medium Temperature not a factor

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**Thermal Noise Current noise density for resistor**

Where does this come from? Assumption: Carriers in thermal equilibrium

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**Thermal Noise in Resistor**

Assumption: Carriers in thermal equilibrium Random velocity vectors v Only vx component contributes to current

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**"Temperature in this room is 293K"**

Boltzmann's Constant k k = 1.38 E-23 J/K Meaning? Thermodynamics: Equipartition theorem Independent energy storage modes in a system at equilibrium have average energy of kT/2 Equivalent statements: "Temperature in this room is 293K" "Average kinetic energy (in each of x, y, z directions) for each air molecule in this room is 2.02E-21 joule"

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**Thermal Noise Approximate collision statistics: Mean free path lc**

Mean free time tc 1 ps Velocity (rms) vx 0.1 µm/ps

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**Thermal Noise Consider "slice" equal to mean free path lc**

During one mean free time tc On average, half of carriers exit each way: IAVG+ = IAVG- Shot noise components is+ = -is- correlated Noise current from "slice" is = 2is+ Sarpeshkar, Delbruck, and Mead, "White noise in MOS transistors and resistors," IEEE Circuits & Devices Magazine, Nov. 1993

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**Thermal Noise Sum (independent) contributions from slices**

Noise current seen by external ammeter im(s) reduced by current divider factor: DR of slice, total resistance R = R1 + DR + R2 Relating to R using mobility definition gives Sarpeshkar, Delbruck, and Mead, "White noise in MOS transistors and resistors," IEEE Circuits & Devices Magazine, Nov. 1993

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**Thermal Noise (Alternative)**

Equipartition, rms energy in capacitor: Integrate noise p.s.d. over noise bandwidth: Equate:

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**Thermal Noise Power Spectral Density**

Key Points: Discrete nature of charge is not essential Can also be derived from equipartition only (e.g. kT/C noise) Carrier scattering: interact with medium, thermal equilibrium Carrier transits are not independent due to interaction with medium Temperature is important to determine carrier average kinetic energy / velocity

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**Overview Creativity in Analog / Mixed Signal IC Design**

DSM CMOS Effects on Analog Design Fundamental Noise Sources Application MOSFET Noise Oscillator Jitter Conclusion

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**MOSFET Channel Noise Density**

Where does this come from? Assumption: Resistive channel segments Y. Tsividis, "Operation and Modeling of the MOS Transistor" New York: Oxford University Press, 2008.

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MOSFET Noise Analysis NOISE DRAIN SOURCE Model: Thermal noise dv for differential segment dx of MOSFET channel Integrate over channel length L Gamma factor g = 2/3 falls out of integral A. Jordan and N. Jordan, "Theory of noise in MOS devices," IEEE Trans. Electron Devices, March, 1965

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**MOSFET Noise Analysis Key assumption:**

Carrier behavior in channel determined by mobility (resistive) behavior What if it's not a resistor? Ask "what if" questions

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**Velocity Saturation Deviation from mobility model at high field**

"High field" Small dimensions Y. Tsividis, "Operation and Modeling of the MOS Transistor" New York: Oxford University Press, 2008.

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**MOSFET Potential Energy (L ~ µm)**

Carrier injection into channel Low field motion modeled by mobility Velocity saturated region

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**MOSFET Potential Energy (L < µm)**

Velocity saturated region is a greater fraction of channel Carriers still interact due to collisions

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**MOSFET Potential Energy (L << µm)**

Channel length L ~ mean free path lc "Ballistic": no interaction due to collisions No thermal equilibrium

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**L < lc "Breaking the Rules"**

L < mean free path lc No thermal equilibrium No reason to expect any validity for a thermal noise / resistance model that assumed mobility and thermal equilibrium Behavior dominated by statistics of carrier injection at source Shot noise! But not full shot noise: Presence of injected carrier modifies potential profile; changes probability of injection

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**Analogy: Bipolar Transistor**

Output current noise ino for isolated bipolar transistor is full shot noise inc of collector current With degeneration resistor: Not full shot noise: Voltage drop across RE modifies vBE ; feedback reduces variation in ino due to inc

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**Submicron CMOS: Noise behavior**

Shot noise prediction Don't interpret as g increase Interpret as shot noise suppression Navid, Lee, and Dutton," A Circuit-Based Noise Parameter Extraction Technique for MOSFETs," ISCAS 2007, pp

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**Overview Creativity in Analog / Mixed Signal IC Design**

DSM CMOS Effects on Analog Design Fundamental Noise Sources Application MOSFET Noise Oscillator Jitter Conclusion

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**Jitter Example: Ring Oscillator**

Time-domain noise (jitter) on clock transitions Characterized by standard deviation (ps rms)

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**Jitter Example: Ring Oscillator**

Plot jitter vs. time interval ∆T Increases as square root: jitter delay frequency-independent figure-of-merit McNeill and Ricketts, "The Designer's Guide to Jitter in Ring Oscillators," Springer, 2009

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**Jitter at the Gate Delay Level**

MOSFET noise adds uncertainty to gate delay Td Statistics of MOSFET noise can be related to oscillator figure-of-merit McNeill and Ricketts, "The Designer's Guide to Jitter in Ring Oscillators," Springer, 2009

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**How to Improve Jitter? Burn more power**

Oscillator figure-of-merit of form Derived from thermal noise model Intuitively, as oscillator power increases, random thermal energy is a smaller fraction of waveform McNeill and Ricketts, "The Designer's Guide to Jitter in Ring Oscillators," Springer, 2009

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**Oscillator Jitter vs. W**

Scales as predicted Chengxin Liu, "Jitter in Oscillators …," PhD Dissertation, WPI, 2006

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**How to Improve Jitter? Burn more power**

Oscillator figure-of-merit of form Derived from thermal noise model How does this behave as L shrinks? McNeill and Ricketts, "The Designer's Guide to Jitter in Ring Oscillators," Springer, 2009

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**Oscillator Jitter vs. L**

? ? Deviation from predicted for L < 1µm Inflection or minimum? Chengxin Liu, "Jitter in Oscillators …," PhD Dissertation, WPI, 2006

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**Overview Creativity in Analog / Mixed Signal IC Design**

DSM CMOS Effects on Analog Design Fundamental Noise Sources Applications Conclusion Learn from every outcome

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**DSM CMOS Conclusions Survey the landscape**

Noise behavior changes for short L Question assumptions Mobility model Ask "what if" questions What if it's not a resistor? Learn from every outcome Jitter example: Scaling may not provide benefits for analog as one might expect from long channel model

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**Design Drivers in DSM CMOS**

Environment: Decreasing ability to predict analog performance from simple assumptions / models Explorer Artist Judge Warrior Add Complexity Eliminate Complexity Digital Analog

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**Acknowledgments WPI David Cyganski Chengxin Liu Analog Devices**

Mike Coln Bob Adams Larry DeVito Colin Lyden Carnegie Mellon David Ricketts Columbia University Yannis Tsividis Creativity Resources Roger von Oech

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**References Creativity MOSFET Device Physics CMOS Design**

R. Von Oech, "A Whack on the Side of the Head" New York: Warner, ISBN R. Von Oech, "A Kick in the Seat of the Pants" New York: HarperCollins, ISBN MOSFET Device Physics Y. Tsividis, "Operation and Modeling of the MOS Transistor" New York: Oxford University Press, ISBN CMOS Design Op 't Eynde and Sansen, "Design and Optimization of CMOS Wideband Amplifiers," Proc. CICC, 1989. Oscillator Jitter J. McNeill and D. Ricketts, "The Designer's Guide to Jitter in Ring Oscillators" New York: Springer, ISBN

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